Generalized S-procedure for inequality conditions on one-vector-lossless sets and linear system analysis

Yoshio Ebihara, Katsutoshi Maeda, Tomomichi Hagiwara

Research output: Contribution to journalConference articlepeer-review

9 Citations (Scopus)

Abstract

The generalized S-procedure, introduced by Iwasaki et al., has proved to be very useful for robustness analysis and synthesis of control systems. This procedure provides a nonconservative way to convert inequality conditions on lossless sets into numerically verifiable conditions represented by linear matrix inequalities (LMIs). In this paper, we introduce a new notion, one-vector-lossless sets, and propose a generalized S-procedure to reduce inequality conditions on one-vector-lossless sets into LMIs without any conservatism. By means of the proposed generalized S-procedure, we can examine various properties of matrix-valued functions over some regions on the complex plane. To illustrate the usefulness, we show that full rank property analysis problems of polynomial matrices over some specific regions on the complex plane can be reduced into LMI feasibility problems. It turns out that many existing results such as Lyapunov's inequalities for stability analysis of linear systems and LMIs for state-feedback controller synthesis can be viewed as particular cases of this result.

Original languageEnglish
Article numberTuC10.3
Pages (from-to)1272-1277
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume2
DOIs
Publication statusPublished - 2004
Externally publishedYes
Event2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas
Duration: Dec 14 2004Dec 17 2004

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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